Question 71
Let $ABC$ be an acute triangle and let $B'$ and $C'$ be the feet of its altitudes from $B$ and $C$, respectively. Let $B_A'$ and $B_C'$ be the reflections of $B'$ in the lines $BC$ and $AB$, respectively. The circle $BB_A'B_C'$, centred at $O_B$, meets the line $AB$ a second time at $X_B$. The points $C_A'$, $C_B'$, $O_C$, $X_C$ are defined analogously, by replacing the pair $(B, B')$ with the pair $(C, C')$. Show that $O_BX_B$ and $O_CX_C$ are parallel.